Observe that
8² = 64
(1/1000)² = 1/1000000 = 0.00001
8² × (1/1000)² = 64 × 0.000001 = 0.000064
Then
[tex](0.000064)^{5/6} = \left(\left(\dfrac8{1000}\right)^2\right)^{5/6} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac8{1000}\right)^{5/3} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac{2^3}{10^3}\right)^{5/3} \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\dfrac2{10}\right)^5 \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{2^5}{10^5} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{32}{100000} = \boxed{\dfrac1{3125} = 0.00032}[/tex]
